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On the distribution of MIMO mutual information: An in-depth painlevé-based characterization
Li S.1; McKay M.R.2; Chen Y.3
2013-08-28
Source PublicationIEEE Transactions on Information Theory
ISSN00189448
Volume59Issue:9Pages:5271-5296
Abstract

This paper builds upon our recent work which computed the moment generating function of the multiple-input multiple-output mutual information exactly in terms of a Painlevé V differential equation. By exploiting this key analytical tool, we provide an in-depth characterization of the mutual information distribution for sufficiently large (but finite) antenna numbers. In particular, we derive systematic closed-form expansions for the high-order cumulants. These results yield considerable new insight, such as providing a technical explanation as to why the well-known Gaussian approximation is quite robust to large signal-to-noise ratio for the case of unequal antenna arrays, while it deviates strongly for equal antenna arrays. In addition, by drawing upon our high-order cumulant expansions, we employ the Edgeworth expansion technique to propose a refined Gaussian approximation which is shown to give a very accurate closed-form characterization of the mutual information distribution, both around the mean and for moderate deviations into the tails (where the Gaussian approximation fails remarkably). For stronger deviations where the Edgeworth expansion becomes unwieldy, we employ the saddle point method and asymptotic integration tools to establish new analytical characterizations which are shown to be very simple and accurate. Based on these results, we also recover key well-established properties of the tail distribution, including the diversity-multiplexing-tradeoff. 

KeywordChannel Capacity Multiple-input Multiple-output (Mimo) Systems Random Matrix Theory
DOI10.1109/TIT.2013.2264505
URLView the original
Indexed BySCI
Language英语
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Information Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000323455800005
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Cited Times [WOS]:10   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Department of Electrical Engineering, Columbia University, New York, NY, USA
2.Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
3.Department of Mathematics, University of Macau, Taipa, China
Recommended Citation
GB/T 7714
Li S.,McKay M.R.,Chen Y.. On the distribution of MIMO mutual information: An in-depth painlevé-based characterization[J]. IEEE Transactions on Information Theory,2013,59(9):5271-5296.
APA Li S.,McKay M.R.,&Chen Y..(2013).On the distribution of MIMO mutual information: An in-depth painlevé-based characterization.IEEE Transactions on Information Theory,59(9),5271-5296.
MLA Li S.,et al."On the distribution of MIMO mutual information: An in-depth painlevé-based characterization".IEEE Transactions on Information Theory 59.9(2013):5271-5296.
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